A Mathematical Graph-Theoretic Model of Single Point Mutations Associated with Sickle Cell Anemia Disease

Edem K Netsey,Dr Samuel Kakraba,Aayire C Yadem,Samuel M Naandam

doi:10.24297/jbt.v9i.9109

Abstract

Many diseases like cystic fibrosis and sickle cell anemia disease (SCD), among others, arise from single point mutations in the respective proteins. How a single point mutation might lead to a global devastating consequence on a protein remains an intellectual mystery. SCD is a genetic blood-related disorder resulting from mutations in the beta chain of the human hemoglobin protein (simply, β-globin), subsequently affecting the entire human body. Higher mortality and morbidity rates have been reported for patients with SCD, especially in sub-Saharan Africa. Clinical management of SCD often requires specialized interdisciplinary clinicians. SCD presents a major global burden, hence an improved understanding of how single point mutations in β-globin results in different phenotypes of SCD might offer insight into protein engineering, with potential therapeutic intervention in view. By use of mathematical modeling, we built a hierarchical (nested) graph-theoretic model for the β-globin. Subsequently, we quantified the network of interacting amino acid residues, representing them as molecular system of three distinct stages (levels) of interactions. Using our nested graph model, we studied the effect of virtual single point mutations in β-globin that results in varying phenotypes of SCD, visualized by unsupervised machine learning algorithm, the dendrogram.

Highlights

Protein engineering requires deep insight into protein folding and misfolding, thereby underscoring the importance of experimental and computational models to study such complex network and systems
We used our graph-theoretic molecular weighted invariants or descriptors computed for the wildtype, mild and severe mutations, and employed a statistical unsupervised machine learning algorithm to visualize how each sickle cell anemia disease (SCD) single point mutation varies from the wildtype for the β-globin
Our choice of the single-linkage function stems from our effort to decrease any possible biases in the clustering of the single point mutations associated with SCD

Summary

Introduction

Protein engineering requires deep insight into protein folding and misfolding, thereby underscoring the importance of experimental and computational models to study such complex network and systems. There is limited understanding of how a single point mutation in the β-globin prevents correct folding and maintenance of hemoglobin and subsequently affects the entire protein. Many diseases including SCD, COVID-19 and neurodegenerative diseases (such as Parkinson’s, Alzheimer’s, Amyotrophic lateral sclerosis) show elevated levels of protein aggregates resulting from mostly severe mutations (Ayyadevara et al, 2017; Balasubramaniam et al, 2019; Kakraba et al, 2019). Mutation in the Huntington gene, Parkinson’s (e.g. LRRK2, PARK7), cystic fibrosis (e.g. N1303K, deltaF508), diabetes mellitus, sickle-cell anemia (e.g. E6V, V23I, K82N, K95E, E6K, E26K) among other diseases, all result from single point mutations in associated proteins (Abou-Sleiman et al, 2004; Chakravorty & Williams, 2015; Chernoff et al, 1954; Erer et al, 2016; Nuytemans et al, 2010)

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Conclusion